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the values can be used for the exit wave reconstruction. Additionally, they offer a higher signal to noise ratio. However, unless atom counting is possible, a correct thickness de-termination remains problematic. Finally, only a few dozen to 100 atoms are present in an atom column small of a sample thin enough for reconstruction. As a result, for the detection of defects with concentrations below a few percent, a large number of phase measurements must be performed to better statistics.

Chapter 6 Summary

New tools are required to analyze novel nanostructured materials at the atomic scale.

Quantitative high resolution transmission electron microscopy (HRTEM) is currently being developed for this purpose. In this thesis, the opportunities and limitations of quantita-tive HRTEM were explored. The technique was then applied to determine the chemical inhomogeneity and clustering that affect the properties of the semiconductors InxGa1−xN, InN and ZnO.

Rules for reliable strain measurement using HRTEM

A methodology for quantitative HRTEM analysis by strain measurement in lattice mis-matched alloys was presented Chapter 2. Three factors for reliable strain measurement were identified: (a) The samples must be free of preparation damage as can be realized by using a wet etching technique or low energy (<500 kV) ion milling. (b) Damage from the imaging beam must be avoided as can be done in InxGa1−xN and other sensitive materials if exposure time is kept below two minutes and beam current density is low (<30 A/cm2).

(c) Imaging artefacts can be avoided by using high voltage microscopes (acceleration volt-age ≥ 800 kV), averaging over series of images or by performing exit wave reconstruction.

With these conditions satisfied, lattice relaxation in wedge shaped TEM samples was accu-rately measured and modelled. Finally, it was shown how clustering can be distinguished from a purely random distribution of atoms in a crystalline alloy.

Decomposition of InxGa1−xN

The distribution of indium atoms in InxGa1−xN alloys was studied in Chapter 3. In InxGa1−xN quantum wells, clustering was detected forx >0.1 while noise did not allow an

tude in InxGa1−xN quantum wells and thick InxGa1−xN films were compared to each other and show identical functional dependencies. This provides strong evidence, that cluster formation in InxGa1−xN quantum wells can be explained by a thermodynamic process sim-ilar to spinodal decomposition in bulk InxGa1−xN. The center of the miscibility gap was placed around x = 0.5 - 0.6.

Infrared resonance of nanoscopic indium clusters in InN

InN samples were searched for nanometer-scale inclusions that can be present below the detection limit of X-ray diffraction. Indeed spots of contrast were found and explained by metallic indium inclusions. The size of the clusters correlates with a change in lumines-cence. The infrared resonances or parallel band transitions of indium clusters may thus strongly influence the optical properties of the InN.

Characterization of homoepitaxial ZnO

Two samples grown on oxygen-face and zinc-face substrates respectively, were studied. In both cases, the polarity is conserved across the interface. The O-face layer exhibits strong compressive strain as well as numerous impurity or defect luminescence lines. The Zn-face is almost relaxed to the substrate and offers better luminescent properties with line widths as narrow as 80 µeV. It is argued that additional impurities or defects are included in epilayers grown on O-face substrates. As a consequence, Zn-face epitaxy seems to produce material of higher quality.

Chapter 7 Outlook

In the years to come, the detection and determination of clustering and chemical (in)homogeneity will be ever more important as structures and devices are miniaturized further. As a result, the structural analysis of materials at an atomic scale will develop into a common need of both research and industry.

Quantitative HRTEM is already a powerful tool due to its high spatial resolution and sensitivity. However, as outlined in this study, it is sometimes necessary to use averaging and statistics to reach a reliable conclusions. In the case of clustering for example, this means that information about the shape of the clusters is discarded. The problem is deepened by the fact, that HRTEM only images a projection of the sample.

An important step to resolve these limitations is currently being undertaken at NCEM with the development of the TEAM microscope. The machine will be corrected for spher-ical and chromatspher-ical aberration and will achieve sub-˚Angstrom resolution at accelerating voltage as low as 80 kV. As a result beam damage will be reduced significantly and samples can be imaged for a much longer time. Exit wave reconstruction can then be performed in different crystallographic orientations. Together with an improved signal to noise ratio al-lowing for single atom counting, atomic scale tomographic reconstruction will then become possible. Among other things, this will finally allow to study the exact shape of indium rich clusters in InxGa1−xN and hopefully lead to an exact explanation of the decomposition in this material.

Even so, the present work showed that the cluster formation in InxGa1−xN is likely due to spinodal decomposition. Because of the small length scales involved (2-5 nm) the continuity model of spinodal decomposition breaks down and it would be interesting to model it at an atomic scale. It might still be thermodynamically impossible to grow

homogenous layers with high indium content. Layers of high quality could still be realized, if a way to nucleate spinodal decomposition in a controlled fashion is found. This could be achieved by a periodical variation of the growing temperature or the In/Ga flow ratio.

Thick InxGa1−xN layers could then decompose into a stack of self formed quantum wells.

Aberration corrected microscopes also have an excellent signal to noise ratio. As a result point defects should be detectable and identifiable by phase changes in the exit wave as was tried in this work for ZnO.

Acknowledgements

Many people and institutions have contributed to the success of this thesis. I would like to thank my Doktorvater Priv. Doz. Dr. Axel Hoffmann for actively supporting me in a somewhat unconventional thesis. His personal mentorship is also much appreciated. It is thanks to his support and the recommendations by Prof. Dr. Dieter Bimberg and Prof. Dr. Marius Grundmann that I was awarded a PhD fellowship. The German National Academic Foundation is gratefully acknowledged. Beside financial support this fellowship provided me with interesting outlooks and contacts into other fields of re-search, that I would have missed otherwise. I would like to thankProf. Dr. Eicke Weber and his group at UC Berkeley for welcoming me so warmly and providing a rewarding an challenging research environment.

Very special thanks go to Dr. Christian Kisielowski and Dr. Petra Specht for a friendship built not only on a very intense collaboration but also on turkey feasts and more than one shared bottle of fine wine. All I know of TEM I learned under Christian’s guidance at the National Center for Electron Microscopy (NCEM). The NCEM user family, namelyQuentin RamasseandYu Satoand many others as well as the staff, in particular Jane Cavlina, ChengYu Song, John Turner and Doreen Ah Tye are remembered for the good times and helpful assistance. NCEM is part of Lawrence Berkeley National Laboratory and supported by the U.S. Department of Energy under Contract #DE-AC02-05CH11231.

I am indebted to Prof. Dr. Michael Lehmannwho has accepted to be co-corrector of my thesis. Together with Dr. Tore Niermann he has proofread this thesis in record time and made valuable comments. Henning Schr¨oder’s corrections are also much ap-preciated. Finally I owe thanks tomy parentswho have simplified my unsteady life style of moving back in forth between continents by always providing me with a stable base to start my operations from. My life partner Gloria Gi Day has always handled this instability with great patience.

Thank You!

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